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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2496n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2496.z2 | 2496n1 | \([0, 1, 0, 8, -10]\) | \(778688/1521\) | \(-97344\) | \([2]\) | \(256\) | \(-0.35830\) | \(\Gamma_0(N)\)-optimal |
2496.z1 | 2496n2 | \([0, 1, 0, -57, -153]\) | \(5088448/1053\) | \(4313088\) | \([2]\) | \(512\) | \(-0.011725\) |
Rank
sage: E.rank()
The elliptic curves in class 2496n have rank \(1\).
Complex multiplication
The elliptic curves in class 2496n do not have complex multiplication.Modular form 2496.2.a.n
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.